Skip to main content
Springer Nature Link
Log in

Composing Stability Proofs for Hybrid Systems

  • Conference paper
Formal Modeling and Analysis of Timed Systems (FORMATS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6919))

Abstract

A recent automatic proof method for the region stability of a hybrid system is based on the reachability analysis for a transformed hybrid system with double dimensionality (the transformation duplicates each of the continuous variables). We propose a new method which composes the reachability analyses for a sequence of transformed hybrid systems with essentially the same dimensionality (each transformation in the sequence duplicates one of the continuous variables). The new method thus trades the double dimensionality for the number of reachability analyses.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bogomolov, S., Mitrohin, C., Podelski, A.: Composing reachability analyses of hybrid systems for safety and stability. In: Bouajjani, A., Chin, W.-N. (eds.) ATVA 2010. LNCS, vol. 6252, pp. 67–81. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  3. Frehse, G.: PHAVer: Algorithmic verification of hybrid systems past hyTech. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 258–273. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  4. Podelski, A., Wagner, S.: Model checking of hybrid systems: From reachability towards stability. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 507–521. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  5. Podelski, A., Wagner, S.: Region stability proofs for hybrid systems. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 320–335. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  6. Podelski, A., Wagner, S.: A sound and complete proof rule for region stability of hybrid systems. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 750–753. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  7. Rybalchenko, A.: RankFinder, http://www.mpi-inf.mpg.de/rybal/rankfinder

  8. Wagner, S.: Stability Proofs for Hybrid Systems. PhD thesis, Universität des Saarlandes (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Freiburg, Freiburg, Germany

    Corina Mitrohin & Andreas Podelski

Authors
  1. Corina Mitrohin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andreas Podelski
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. IRISA/INRIA Rennes, Campus Beaulieu, 35042, Rennes Cedex, France

    Uli Fahrenberg

  2. University of California, 94720-1770, Berkeley, CA, USA

    Stavros Tripakis

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mitrohin, C., Podelski, A. (2011). Composing Stability Proofs for Hybrid Systems. In: Fahrenberg, U., Tripakis, S. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2011. Lecture Notes in Computer Science, vol 6919. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24310-3_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-24310-3_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24309-7

  • Online ISBN: 978-3-642-24310-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics